If a^ and b^ are non-collinear unit vectors and if a^+b^=3, then the value of 2a→-5b→.3a→+b→

A
$\frac{41}{2}$
B
$\frac{11}{2}$
C
- $\frac{11}{2}$
D
- $\frac{41}{2}$

Solution:

$|\hat{a} + \hat{b}| = \sqrt{3} \Rightarrow \sqrt{1^{2} {+1}^{2} +2 (1)(1) cosθ} = \sqrt{3}$
$\Rightarrow cosθ = \frac{1}{2} \Rightarrow θ = 60^{o}$
$(2 \hat{a} - 5 \hat{b}) . (3 \hat{a} + \hat{b}) = 6 + 2 \hat{a} . \hat{b} - 15 \hat{a} . \hat{b} - 5$
$=1 - 13 cosθ=1- \frac{13}{2} = - \frac{11}{2}$

If $\hat{a}$ and $\hat{b}$ are non-collinear unit vectors and if $|\hat{a} + \hat{b}| = \sqrt{3}$ , then the value of $(2 \vec{a} - 5 \vec{b}) . (3 \vec{a} + \vec{b})$

Solution:

Related content