What is the value of k for which the vector k(2î - ĵ - 2k̂) is of 6 units length?

Question

Question

Answer 1

Concept:

Length of the vector \(\rm a\hat{i} + b\hat{j} + c\hat{k} \) from origin is \(\rm \sqrt{a^{2} + b^{2} + c^{2}}\)

Calculation:

Length of the vector k(2î - ĵ - 2k̂) from origin is

\(\rm \sqrt{(2k)^{2} + (-k)^{2} + (-2k)^{2}}\)

= \(\rm \sqrt{4k^{2} + k^{2} + 4k^{2}}\)

= \(\rm \sqrt{9k^{2} }\)

= 3k

Length is 6 units given

3k = 6

k = 6/3

k = 2

Hence option 2 is correct.