Question

If r is a vector of magnitude 21 and has d.r.’s 2, –3, 6. Then r is equal to

• A.
• B.
• C. $6 i - 9 j - 18 k$
• D.

Answer 1

Answer: (A)

Answer 2

D.r.’s of r are 2, –3, 6.

Therefore, its d.c.’s are $l = \frac { 2 } { 7 } , m = \frac { - 3 } { 7 } , n = \frac { 6 } { 7 }$

∴ $\mathbf { r } = | \mathbf { r } | ( \mathbf { i } + m \mathbf { j } + n \mathbf { k } ) = 21 \left[ \frac { 2 } { 7 } \mathbf { i } - \frac { 3 } { 7 } \mathbf { j } + \frac { 6 } { 7 } \mathbf { k } \right] = 6 \mathbf { i } - 9 \mathbf { j } + 18 \mathbf { k }$ .