First slide

Vectors

Question

If |A| = 2 and |B| = 4, then match the relation in Column I with the angle $θ$ between A and B in column II.
Column I Column II
(p) A.B = 0 (i) $θ$ = 0
(q) A.B = +8 (ii) $θ$ = $90^{0}$
r A.B = 4 (iii) $θ = 180^{0}$
(s) A.B = -8 (iv) $θ = 60^{0}$
Now, mark the correct choice from the given codes.
Codes

Moderate

A

p-ii, q-i, r-iv, s-iii
B

p-iv, q- iii, r-i, s-ii
C

p-i, q-iii, r-iv, s-ii
D

p-iii, q-iv, r-i, s- ii

Solution

Given |A| = 2 and |B| = 4
(p) A.B = $ABcosθ = 0 \Rightarrow 2 \times 4 cosθ = 0$
$\Rightarrow cosθ = 0 = \cos 90^{0} \Rightarrow θ = 90^{0}$
Thus, option (p) matches with option (ii).
(q) A.B = $AB cosθ = 8 \Rightarrow 2 \times 4 cosθ = 8$
$\Rightarrow cosθ = 1 = \cos 0^{0} \Rightarrow θ = 0^{0}$
Thus, option (q) matches with option (i),
r) $A . B = AB cosθ = 4 \Rightarrow 2 \times 4 cosθ = 4$
$\Rightarrow cosθ = \frac{1}{2} = \cos 60^{0} \Rightarrow θ = 60^{0}$
Thus, option r) matches with option (iv).
(s). A.B = $ABcosθ = - 8 \Rightarrow 2 \times 4 cosθ = - 8$
$\Rightarrow cosθ = - 1 = \cos [180^{0}] \Rightarrow θ = 180^{0}$
Thus, option (s) matches with option (iii).

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