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Maths-

General

Easy

Question

If $vertical line a cross times b vertical line equals 4$ and $vertical line a. b vertical line equals 2$ , then $vertical line a vertical line to the power of 2 end exponent vertical line b vertical line to the power of 2 end exponent equals$

2
6
8
20

The correct answer is: 20

Given $vertical line a cross times b vertical line equals 4$ $rightwards double arrow open vertical bar vertical line a vertical line vertical line b vertical line sin invisible function application theta stack n with hat on top close vertical bar equals 4$
$rightwards double arrow open vertical bar rightwards arrow over short leftwards arrow vertical line a vertical line vertical line b vertical line sin invisible function application theta close vertical bar equals 4$ …..(i)
Also $vertical line a. b vertical line equals 2$ $rightwards double arrow open vertical bar vertical line a vertical line vertical line b vertical line cos invisible function application theta close vertical bar equals 2$
$rightwards double arrow open vertical bar vertical line a vertical line vertical line b vertical line cos invisible function application theta close vertical bar equals 2$ …..(ii)
Now squaring and adding equation (i) and (ii), we get
$vertical line a vertical line to the power of 2 end exponent. vertical line b vertical line to the power of 2 end exponent sin to the power of 2 end exponent invisible function application theta plus vertical line a vertical line to the power of 2 end exponent. vertical line b vertical line to the power of 2 end exponent cos to the power of 2 end exponent invisible function application theta equals 4 to the power of 2 end exponent plus 2 to the power of 2 end exponent$
$therefore vertical line a vertical line to the power of 2 end exponent. vertical line b vertical line to the power of 2 end exponent left parenthesis sin to the power of 2 end exponent invisible function application theta plus cos to the power of 2 end exponent invisible function application theta right parenthesis equals 16 plus 4$
$rightwards double arrow vertical line a vertical line to the power of 2 end exponent. vertical line b vertical line to the power of 2 end exponent cross times 1 equals 20.$

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