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Question: If \(\theta\) be the angle between the vectors \(\mathbf { a } = 2 \mathbf { i } + 2 \mathbf { j } -...

If θ\theta be the angle between the vectors a=2i+2j−k\mathbf { a } = 2 \mathbf { i } + 2 \mathbf { j } - \mathbf { k } and , then

A

cos⁡θ=421\cos \theta = \frac { 4 } { 21 }

B

cos⁡θ=319\cos \theta = \frac { 3 } { 19 }

C

cos⁡θ=219\cos \theta = \frac { 2 } { 19 }

D

cos⁡θ=521\cos \theta = \frac { 5 } { 21 }

Answer

cos⁡θ=421\cos \theta = \frac { 4 } { 21 }

Explanation

Solution

Angle between a\mathbf { a } and is given by,

= 12−6−23.7=421\frac { 12 - 6 - 2 } { 3.7 } = \frac { 4 } { 21 }