If a- and b- are vectors such that -a-b-29 and a- 2 -3 -4 k-2 - - 3 -4k- -b- then a possible value of a- - b-7 -2 - - 3 k- is

A⃗×b⃗ = a⃗×c⃗ ⇒a⃗×b⃗ a⃗×c⃗ =0 ⇒a⃗||b⃗ c⃗) or b⃗ c⃗=λa⃗ Here, a⃗× (2 î+3 ĵ+4 k̂)=(2 î+3 ĵ+4 k̂) ×b⃗ ⇒ a⃗× (2 î+3 ĵ+4 k̂) (2 î+3 ĵ+4 k̂) ×b⃗=0 ⇒ (a⃗+b⃗) × (2 î+3 ...

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Byju's Answer

Standard XII

Mathematics

Cross Product of Two Vectors

If a⃗ and b⃗ ...

Question

If $\to a$ and $\to b$ are vectors such that $| \to a + \to b | = \sqrt{29}$ and $\to a \times (2^i + 3^j + 4^k) = (2^i + 3^j + 4^k) \times \to b,$ then a possible value of $(\to a + \to b) . (- 7^i + 2^j + 3^k)$ is

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Solution

The correct option is C
4

$\to a \times \to b = \to a \times \to c \Rightarrow \to a \times \to b - \to a \times \to c = 0 \Rightarrow \to a | | \to b - \to c) or \to b - \to c = λ \to a Here, \to a \times (2^i + 3^j + 4^k) = (2^i + 3^j + 4^k) \times \to b \Rightarrow \to a \times (2^i + 3^j + 4^k) - (2^i + 3^j + 4^k) \times \to b = 0 \Rightarrow (\to a + \to b) \times (2^i + 3^j + 4^k) = 0 \Rightarrow \to a + \to b = λ (2^i + 3^j + 4^k) Since, | \to a + \to b | = \sqrt{29} \Rightarrow \pm λ \sqrt{4 + 9 + 16} = \sqrt{29} \Rightarrow λ = \pm 1 ∴ \to a + \to b = \pm (2^i + 3^j + 4^k) Now, (\to a + \to b) . (- 7^i + 2^j + 3^k) = \pm (- 14 + 6 + 12) = \pm 4$

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If →a and →b are vectors such that |→a+→b|=√29 and →a×(2^i+3^j+4^k)=(2^i+3^j+4^k)×→b, then a possible value of (→a+→b).(−7^i+2^j+3^k) is

If $\to a$ and $\to b$ are vectors such that $| \to a + \to b | = \sqrt{29}$ and $\to a \times (2^i + 3^j + 4^k) = (2^i + 3^j + 4^k) \times \to b,$ then a possible value of $(\to a + \to b) . (- 7^i + 2^j + 3^k)$ is