Find the value of - such that the vectors a -2 -k- and b -2 -3 k- are orthogonal-a 0bc 3-2d -5-2

Since, two non zero vectors a and b are orthogonal i.e., a.b=0 ∴ (2î+λĵ+k̂).(î+2ĵ+3k̂)=0 ⇒ 2+2λ+3=0 ∴ λ= 5/2 ...

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Standard XII

Mathematics

Bisector of Angle between Two Vectors

Find the valu...

Question

Find the value of $λ$ such that the vectors $\to a = 2^i + λ^j +^k a n d \to b =^i + 2^j + 3^k$ are orthogonal.

(a) 0

(b) 1

(c) $\frac{3}{2}$

(d) $\frac{- 5}{2}$

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Solution

Since, two non-zero vectors $\to a a n d \to b$ are orthogonal i.e., $\to a . \to b = 0$

$∴ (2^i + λ^j +^k) . (^i + 2^j + 3^k) = 0 \Rightarrow 2 + 2 λ + 3 = 0 ∴ λ = \frac{- 5}{2}$

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Find the value of λ such that the vectors →a=2^i+λ^j+^k and →b=^i+2^j+3^k are orthogonal. (a) 0 (b) 1 (c) 32 (d) −52

Since, two non-zero vectors →a and →b are orthogonal i.e., →a.→b=0 ∴ (2^i+λ^j+^k).(^i+2^j+3^k)=0⇒ 2+2λ+3=0∴ λ=−52

Find the value of $λ$ such that the vectors $\to a = 2^i + λ^j +^k a n d \to b =^i + 2^j + 3^k$ are orthogonal.

(a) 0

(b) 1

(c) $\frac{3}{2}$

(d) $\frac{- 5}{2}$

Since, two non-zero vectors $\to a a n d \to b$ are orthogonal i.e., $\to a . \to b = 0$

$∴ (2^i + λ^j +^k) . (^i + 2^j + 3^k) = 0 \Rightarrow 2 + 2 λ + 3 = 0 ∴ λ = \frac{- 5}{2}$