Vectors a hati+b hatj+ hatk and 2 hati-3 hatj+4 hatk are perpendicular to each other when 3 a+2 b=7, the ratio of a to b is (x/2) The value of x is

Question

Vectors a hati+b hatj+ hatk and 2 hati-3 hatj+4 hatk are perpendicular to each other when 3 a+2 b=7, the ratio of a to b is (x/2) The value of x is  (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

For two perpendicular vectors (a hati+b hatj+ hatk) ⋅(2 hati-3 hatj+4 hatk)=0 2 a-3 b+4=0 On solving, 2 a-3 b=-4 Also given 3 a +2 b =7 We get a =1, b =2 (a/b)=(x/2) ⇒ x=(2 a/b)=(2 × 1/2) ⇒ x=1

Q. Vectors ai^+bj^​+k^ and 2i^−3j^​+4k^ are perpendicular to each other when 3a+2b=7, the ratio of a to b is 2x​ The value of x is __

For two perpendicular vectors (ai^+bj^​+k^)⋅(2i^−3j^​+4k^)=0 2a−3b+4=0 On solving, 2a−3b=−4 Also given 3a+2b=7 We get a=1,b=2 ba​=2x​⇒x=b2a​=22×1​ ⇒x=1

Q. Vectors $a \hat{i} + b \hat{j} + \hat{k}$ and $2 \hat{i} - 3 \hat{j} + 4 \hat{k}$ are perpendicular to each other when $3 a + 2 b = 7$ , the ratio of $a$ to $b$ is $\frac{x}{2}$ The value of $x$ is __