Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Offsite Campus Turito Championship

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Maths-

General

Easy

Question

Let , ,  be distinct real numbers. The points with position vectors $alpha stack i with hat on top$ + $beta stack j with hat on top$ + $gamma stack k with hat on top$ , $beta stack i with hat on top$ + $gamma stack j with hat on top$ + $alpha stack k with hat on top$ , $gamma stack i with hat on top$ + $alpha stack j with hat on top$ + $beta stack k with hat on top$

are collinear
form an equilateral triangle
form a scalene triangle
form a right angled triangle

The correct answer is: form an equilateral triangle

A ( $stack a with rightwards arrow on top$ =  $stack i with hat on top$ +  $stack j with hat on top$ +  $stack k with hat on top$ )
B ( $stack b with rightwards arrow on top$ = $beta stack i with hat on top$ + $gamma stack j with hat on top$ + $alpha stack k with hat on top$ )
C ( $stack c with rightwards arrow on top$ = $gamma stack i with hat on top$ + $alpha stack j with hat on top$ + $beta stack k with hat on top$ )
AB = $vertical line stack A B with rightwards arrow on top vertical line$ = $square root of left parenthesis alpha – beta right parenthesis to the power of 2 end exponent plus left parenthesis beta – gamma right parenthesis to the power of 2 end exponent plus left parenthesis gamma – alpha right parenthesis to the power of 2 end exponent end root$
= BC = | $stack B C with rightwards arrow on top$ |
= CA = | $stack C A with rightwards arrow on top$ |
 ABC is an equilateral triangle.

Related Questions to study

ABCD is a parallelogram and P is the intersection point of diagonals. If O is any point in the plane of the parallelogram, then
$stack O A with rightwards arrow on top$ + $stack O B with rightwards arrow on top$ + $stack O C with rightwards arrow on top$ + $stack O D with rightwards arrow on top$ must be equal to -

ABCD is a parallelogram and P is the intersection point of diagonals. If O is any point in the plane of the parallelogram, then
$stack O A with rightwards arrow on top$ + $stack O B with rightwards arrow on top$ + $stack O C with rightwards arrow on top$ + $stack O D with rightwards arrow on top$ must be equal to -

The non-zero vectors $stack a with rightwards arrow on top$ ¸ $stack b with rightwards arrow on top$ and $stack c with rightwards arrow on top$ are related by $stack a with rightwards arrow on top$ = 8 $stack b with rightwards arrow on top$ and $stack c with rightwards arrow on top$ = – 7 $stack b with rightwards arrow on top$ . Then the angle between $stack a with rightwards arrow on top$ and $stack c with rightwards arrow on top$ is -

The non-zero vectors $stack a with rightwards arrow on top$ ¸ $stack b with rightwards arrow on top$ and $stack c with rightwards arrow on top$ are related by $stack a with rightwards arrow on top$ = 8 $stack b with rightwards arrow on top$ and $stack c with rightwards arrow on top$ = – 7 $stack b with rightwards arrow on top$ . Then the angle between $stack a with rightwards arrow on top$ and $stack c with rightwards arrow on top$ is -

The position vectors of P and Q are respectively $stack a with rightwards arrow on top$ and $stack b with rightwards arrow on top$ . If R is a opint on $stack P Q with left right arrow on top$ such that $stack P R with rightwards arrow on top$ = 5 $stack P Q with rightwards arrow on top$ , then the position vector of R is -

The position vectors of P and Q are respectively $stack a with rightwards arrow on top$ and $stack b with rightwards arrow on top$ . If R is a opint on $stack P Q with left right arrow on top$ such that $stack P R with rightwards arrow on top$ = 5 $stack P Q with rightwards arrow on top$ , then the position vector of R is -

parallel

Points A ( $2 stack i with hat on top$ – $stack j with hat on top$ + $stack k with hat on top$ ), B( $stack i with hat on top$ – $3 stack j with hat on top$ – $5 stack k with hat on top$ ), C( $3 stack i with hat on top$ – $4 stack j with hat on top$ – $4 stack k with hat on top$ ) are the vertices of -

Points A ( $2 stack i with hat on top$ – $stack j with hat on top$ + $stack k with hat on top$ ), B( $stack i with hat on top$ – $3 stack j with hat on top$ – $5 stack k with hat on top$ ), C( $3 stack i with hat on top$ – $4 stack j with hat on top$ – $4 stack k with hat on top$ ) are the vertices of -

If $stack a with rightwards arrow on top. stack i with hat on top equals stack a with rightwards arrow on top. left parenthesis stack i with hat on top plus stack j with hat on top right parenthesis equals a. left parenthesis stack i with hat on top plus stack j with hat on top plus stack k with hat on top right parenthesis$ , then $stack a with rightwards arrow on top$ is equal to-

If $stack a with rightwards arrow on top. stack i with hat on top equals stack a with rightwards arrow on top. left parenthesis stack i with hat on top plus stack j with hat on top right parenthesis equals a. left parenthesis stack i with hat on top plus stack j with hat on top plus stack k with hat on top right parenthesis$ , then $stack a with rightwards arrow on top$ is equal to-

If angle between $stack a with rightwards arrow on top$ and $stack b with rightwards arrow on top$ is obtuse, then

If angle between $stack a with rightwards arrow on top$ and $stack b with rightwards arrow on top$ is obtuse, then

parallel

The position vectors of P and Q are respectively $stack a with rightwards arrow on top$ and $stack b with rightwards arrow on top$ . If R is a point on $Error converting from MathML to accessible text.$ such that $Error converting from MathML to accessible text.$ = 5 $Error converting from MathML to accessible text.$ , then the position vector of R is

The position vectors of P and Q are respectively $stack a with rightwards arrow on top$ and $stack b with rightwards arrow on top$ . If R is a point on $Error converting from MathML to accessible text.$ such that $Error converting from MathML to accessible text.$ = 5 $Error converting from MathML to accessible text.$ , then the position vector of R is

A small piece of metal wire is dragged across the gap between the poles of a magnet in 0.4 s. If change in magnetic flux in the wire is $8 cross times 10 to the power of negative 4 end exponent$ Wb, then emf induced in the wire is

A small piece of metal wire is dragged across the gap between the poles of a magnet in 0.4 s. If change in magnetic flux in the wire is $8 cross times 10 to the power of negative 4 end exponent$ Wb, then emf induced in the wire is

Physics-General

A coil of wire of a certain radius has 600 turns and a self inductanceof $108 blank m H$ . The self inductance of a 2^nd similar coil of 500 turns will be

A coil of wire of a certain radius has 600 turns and a self inductanceof $108 blank m H$ . The self inductance of a 2^nd similar coil of 500 turns will be

Physics-General

parallel

If a current of $10 blank A$ flows in one second through a coil, and the induced e.m.f. is $10 blank V$ , then the self-inductance of the coil is

If a current of $10 blank A$ flows in one second through a coil, and the induced e.m.f. is $10 blank V$ , then the self-inductance of the coil is

Physics-General

A transformer of efficiency 90% draws an input power of 4 kW. An electrical appliance connected across the secondary draws a current of 6 A. The impedance of the device is

A transformer of efficiency 90% draws an input power of 4 kW. An electrical appliance connected across the secondary draws a current of 6 A. The impedance of the device is

Physics-General

If $negative 7 less than x less or equal than 0$ and $negative 9 less or equal than x less than 2$ then x $element of$

If $negative 7 less than x less or equal than 0$ and $negative 9 less or equal than x less than 2$ then x $element of$

parallel

Let a, b, c be distinct non-negative numbers. If the vectors ai + aj + ck, i + k and ci + cj + bk lie in a plane, then c is -

Let a, b, c be distinct non-negative numbers. If the vectors ai + aj + ck, i + k and ci + cj + bk lie in a plane, then c is -

Let a, b and c be three non-coplanar vectors, and let p, q and r be the vectors defined by the relations p = $fraction numerator b cross times c over denominator left square bracket a b c right square bracket end fraction$ . q = $fraction numerator c cross times a over denominator left square bracket a b c right square bracket end fraction$ and r = $fraction numerator a cross times b over denominator left square bracket a b c right square bracket end fraction blank$ Then the value of the expression (a + b).p + (c + a).r is equal to -

Let a, b and c be three non-coplanar vectors, and let p, q and r be the vectors defined by the relations p = $fraction numerator b cross times c over denominator left square bracket a b c right square bracket end fraction$ . q = $fraction numerator c cross times a over denominator left square bracket a b c right square bracket end fraction$ and r = $fraction numerator a cross times b over denominator left square bracket a b c right square bracket end fraction blank$ Then the value of the expression (a + b).p + (c + a).r is equal to -

The vectors c, directed along the internal bisector of the angle between the vectors a = 7i – 4j – 4k and b = – 2i – j + 2k , with |c| = 5 $square root of 6$ is -

The vectors c, directed along the internal bisector of the angle between the vectors a = 7i – 4j – 4k and b = – 2i – j + 2k , with |c| = 5 $square root of 6$ is -

parallel

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.