If a vector 2 hati+4 hatj+6 hatk is perpendicular to the vector 5 hati+6 hatj-a hatk. Then the value of a is:

Question

If a vector 2 hati+4 hatj+6 hatk is perpendicular to the vector 5 hati+6 hatj-a hatk. Then the value of a is: (A) 14 / 3 (B) 17 / 9 (C) 14 / 5 (D) 17 / 3

Tardigrade Admin · Accepted Answer

When the vectors are perpendicular to each other then their dot product is equal to zero (2 hat i +4 hat j +6 hat k ) ⋅(5 hat i +6 hat j - a hat k )=0 10+24-6 a =0 34=6 a a =(17/3)

Q. If a vector $2 \hat{i} + 4 \hat{j} + 6 \hat{k}$ is perpendicular to the vector $5 \hat{i} + 6 \hat{j} - a \hat{k}$ . Then the value of a is:

$14/3$

$17/9$

$14/5$

$17/3$

When the vectors are perpendicular to each other then their dot product is equal to zero
$(2 \hat{i} + 4 \hat{j} + 6 \hat{k}) \cdot (5 \hat{i} + 6 \hat{j} - a \hat{k}) = 0$
$10 + 24 - 6 a = 0$
$34 = 6 a$
$a = \frac{17}{3}$

Q. If a vector 2i^+4j^​+6k^ is perpendicular to the vector 5i^+6j^​−ak^. Then the value of a is:

14/3

17/9

14/5

17/3