If overline{a}=2 hat{i}+3 hat{j}+2 hat{k},ove | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) Let $\overline{d} = \overline{a} + \lambda \overline{b}$.$\overline{d} = (2 \hat{i} + 3 \hat{j} + 2 \hat{k}) + \lambda(2 \hat{i} + \hat{j} - \hat{

Vedclass · Accepted Answer

$\frac{-11}{5}$

Vedclass · Answer

(C) Let $\overline{d} = \overline{a} + \lambda \overline{b}$.$\overline{d} = (2 \hat{i} + 3 \hat{j} + 2 \hat{k}) + \lambda(2 \hat{i} + \hat{j} - \hat{k})$$\overline{d} = (2 + 2\lambda) \hat{i} + (3 + \lambda) \hat{j} + (2 - \lambda) \hat{k}$.Since $\overline{d}$ is perpendicular to $\overline{c}$,their dot product must be zero,i.e.,$\overline{c} \cdot \overline{d} = 0$.$(\hat{i} + 3 \hat{j}) \cdot [(2 + 2\lambda) \hat{i} + (3 + \lambda) \hat{j} + (2 - \lambda) \hat{k}] = 0$.$1(2 + 2\lambda) + 3(3 + \lambda) + 0(2 - \lambda) = 0$.$2 + 2\lambda + 9 + 3\lambda = 0$.$5\lambda + 11 = 0$.$\lambda = -\frac{11}{5}$.

If $\overline{a}=2 \hat{i}+3 \hat{j}+2 \hat{k}$,$\overline{b}=2 \hat{i}+\hat{j}-\hat{k}$ and $\overline{c}=\hat{i}+3 \hat{j}$ are such that $(\overline{a}+\lambda \overline{b})$ is perpendicular to $\overline{c}$,then the value of $\lambda$ is

Similar Questions

If $\theta$ is the angle between the vectors $4 \hat{i}-\hat{j}+2 \hat{k}$ and $\hat{i}+3 \hat{j}-2 \hat{k}$, then $\sin 2 \theta=$

The least positive integral value of $\alpha$,for which the angle between the vectors $\alpha \hat{i}-2 \hat{j}+2 \hat{k}$ and $\alpha \hat{i}+2 \alpha \hat{j}-2 \hat{k}$ is acute,is

The orthogonal projection of vector $a$ on vector $b$ is given by:

Evaluate the product $(3 \vec{a}-5 \vec{b}) \cdot (2 \vec{a}+7 \vec{b})$.

$A$ unit vector in the plane of the vectors $2i + j + k$ and $i - j + k$ and orthogonal to $5i + 2j + 6k$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module