Question

If $\overrightarrow{A}=\hat{i}+2\overrightarrow{j}+3\hat{k},\overrightarrow{B}=-\hat{i}+2\hat{j}+\hat{k},\overrightarrow{C}=3\hat{i}+j$ and $\overrightarrow{A}+1\overrightarrow{B}$ is perpendicular to $\overrightarrow{\mathrm{C}},$ thent is equal to

• (A) -5
• (B) 4
• (C) 5
• (D) -4

Answer 1

The Correct Option is C

Explanation:
Now,$$\begin{array}{l}\overrightarrow{\mathbf{A}}+t\overrightarrow{\mathbf{B}}=(1-t)\hat{\mathbf{i}}+(2+2t)\hat{\mathbf{j}}+(3+t)\hat{\mathbf{k}}\\ (\overrightarrow{\mathbf{A}}+t\overrightarrow{\mathbf{B}})\cdot \overrightarrow{\mathbf{C}}=3(1-t)+2+2t=0\\ \Rightarrow -3t+2t+3+2=0\\ \Rightarrow -t=-5\Rightarrow t=5\end{array}$$