Let a→, b→ and c→ be three vectors such that a→=√2, b→=4, c→=1 and b→×c→=√15. If b→=2c→+λa→, then the value of λ is equal to (here, the angle between…

Question

Let a→, b→ and c→ be three vectors such that a→=√2, b→=4, c→=1 and b→×c→=√15. If b→=2c→+λa→, then the value of λ is equal to (here, the angle between b→ and c→ is acute)

MARKS Content Team · Accepted Answer

Correct answer: (C) ±2√2. b→-2c→=λa→ ⇒b→-2c→^2=λa→^2 ⇒b→^2+4c→^2-4b→.c→=λ^22 ⇒16+4-4b→.c→=2λ^2⇒λ^2=10-2b→.c→ ... 1 Now, b→×c→^2+b→.c→^2=b→^2c→^2 15+b→.c→^2=16 ⇒b→.c→=±1 The angle between b→ and c→ is acute Hence, b→.c→=1 from 1 λ^2=8⇒λ=±2√2

Let $\vec{a}, \vec{b}$ and $\vec{c}$ be three vectors such that $|\vec{a}| = \sqrt{2}, |\vec{b}| = 4, |\vec{c}| = 1$ and $|\vec{b} \times \vec{c}| = \sqrt{15} .$ If $\vec{b} = 2 \vec{c} + λ \vec{a}$ , then the value of $λ$ is equal to (here, the angle between $\vec{b}$ and $\vec{c}$ is acute)

Solution

More Vector Algebra Questions

Let a→, b→ and c→ be three vectors such that a→=2, b→=4, c→=1 and b→×c→=15. If b→=2c→+λa→, then the value of λ is equal to (here, the angle between b→ and c→ is acute)

Solution

More Vector Algebra Questions

Let $\vec{a}, \vec{b}$ and $\vec{c}$ be three vectors such that $|\vec{a}| = \sqrt{2}, |\vec{b}| = 4, |\vec{c}| = 1$ and $|\vec{b} \times \vec{c}| = \sqrt{15} .$ If $\vec{b} = 2 \vec{c} + λ \vec{a}$ , then the value of $λ$ is equal to (here, the angle between $\vec{b}$ and $\vec{c}$ is acute)