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CBSE Class 12 Math 2009 Solved Paper

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Question : 6 of 29
Marks: +1, -0
Find the projection of a⃗\vec{a} on b⃗\vec{b} if a⃗.b⃗\vec{a}.\vec{b} = 8 and b⃗\vec{b} = 2i^+6j^+3k^2\hat{i}+ 6\hat{j} +3\hat{k}
Solution:  
Projection of a⃗\vec{a} on b⃗\vec{b} is given by a⃗.b⃗∣b⃗∣\frac{\vec{a}.\vec{b}}{|\vec{b}|} (i)
Given a⃗.b⃗{\vec{a}.\vec{b}} = and b⃗\vec{b} = 2i^+6j^+3k^2\hat{i}+6\hat{j}+3\hat{k}
∣b⃗∣|\vec{b}| = 4+36+9\sqrt{4+36+9} = 7
Substituting value in (i) we get
Projection of a⃗\vec{a} on b⃗\vec{b} = 87\frac{8}{7}
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