If a vector is such that (\overrightarrow { \mathbf { r }... | MATH - VECTOR OR CROSS PRODUCT OF TWO VECTORS AND ITS APPLICATIONS | SolveeIt | Solveeit

Today, August 18

Question

If a vector is such that $\overrightarrow { \mathbf { r } }$ × (i + 2j –k) = i – k then can be equal to –

A

3i + 7j + 3k

B

i + 4j + k

C

i + (t + 3)j + k (where 't' is a scalar)

D

i + 6j + k

Answer

3i + 7j + 3k

Explanation

Solution

Let $\overrightarrow { \mathbf { r } }$ = xi + yj + zk \ × (i + 2j – k) = i – k

Ž (y – 2z)i – j (x – z) + k(x –2y) = i – k

Compare

\ $\overrightarrow { \mathbf { r } }$ = xi + (2x + 1)j + xk for any x.