If a vector 2 i +3 j +8 k is perpendicular to the vector 4 j -4 i +α k then the value of α is:

Correct answer: B. - (1)/(2) a =2 i +3 i +8 k , b=4 j +3 i +α k aligned & a · b =0, if a^ -1 · b^ -1 & (2 i +3 j +8 k ) ·(-4 i+4 j+α k)=(1)/(2) & α=-(1)/(2) aligned

NEET 2005

Exam: NEET
Year: 2005
Subject: Physics
Chapter: Mathematics in Physics

NEET 2005 · Physics · Mathematics in Physics

If a vector 2 i +3 j +8 k is perpendicular to the vector 4 j -4 i...

If a vector

2 \hat{i}+3 \hat{j}+8 \hat{k}

is perpendicular to the vector

4 \hat{j}-4 \hat{i}+\alpha \hat{k}

then the value of

\alpha

is:

Options

A $\frac{1}{2}$
B $- \frac{1}{2}$
C1
D-1

Correct answer

B. $- \frac{1}{2}$

Step-by-step solution

\vec{a}=2 \hat{i}+3 \hat{i}+8 \hat{k}, b=4 \hat{j}+3 \hat{i}+\alpha \hat{k}

\begin{aligned} & \vec{a} \cdot \vec{b}=0, \text{ if } a^{-1} \cdot b^{-1} \\ & \therefore(2 \hat{i}+3 \hat{j}+8 \hat{k}) \cdot(-4 i+4 j+\alpha k)=\frac{1}{2} \\ & \Rightarrow \alpha=-\frac{1}{2} \end{aligned}

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