Vector Algebra · Mathematics · COMEDK

$$ \text { If } \hat{\imath}+\hat{\jmath}-\hat{k} \quad \&~ 2 \hat{\imath}-3 \hat{\jmath}+\hat{k} \text { are adjacent sides of a parallelogram, then length of its diagonals are } $$

Find the value of '$$b$$' such that the scalar product of the vector $$\hat{\imath}+\hat{\jmath}+\hat{k}$$ with the unit vector parallel to the sum of the vectors $$2 \hat{\imath}+4 \hat{\jmath}-5 \hat{k}$$ and $$b \hat{\imath}+2 \hat{\jmath}+3 \hat{k}$$ is unity

Let a, b, c be three vector such that $$a \neq 0$$ and $$\vec{a} \times \vec{b}=2 \vec{a} \times \vec{c},|a|=|c|=1,|b|=4$$ and $$|\vec{b} \times \vec{c}|=\sqrt{15}$$. If $$\vec{b}-2 \vec{c}=\lambda \vec{a}$$ then $$\lambda$$ equals to

$$ \text { The angle between } \hat{\imath}-\hat{\jmath} ~\&~ \hat{\jmath}-\hat{k} \text { is } $$

The vector $$(\vec{r})$$ whose magnitude is $$3 \sqrt{2}$$ units which makes an angle of $$\frac{\pi}{4}$$ and $$\frac{\pi}{2}$$ with $$y$$ and $$z$$- axis respectively is

$$ \text { If }|\vec{a} \times \vec{b}|^2+|\vec{a} \cdot \vec{b}|^2=144 ~\&~|\vec{a}|=4 \text { then }|\vec{b}|= $$

The angle between the vectors $$\mathbf{a}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}$$ and $$\mathbf{b}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}$$ is

If the vectors $$\mathbf{a}=2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}} ; \mathbf{b}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}$$ and $$\mathbf{c}=m \hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$$ are coplanar, then the value of $$m$$ is

$$\mathbf{a}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}-\hat{\mathbf{j}}$$ and $$\mathbf{c}=5 \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}$$, then unit vector parallel to $$\mathbf{a}+\mathbf{b}-\mathbf{c}$$ but in opposite direction is

The scalar components of a unit vector which is perpendicular to each of the vectors $$\hat{\imath}+2 \hat{\jmath}-\hat{k}$$ and $$3 \hat{\imath}-\hat{\jmath}+2 \hat{k}$$ are

$$ \text { If } \vec{a} \text { and } \vec{b} \text { are unit vectors, then the angle between } \vec{a} \text { and } \vec{b} \text { for which } a-\sqrt{2} \vec{b} \text { is a unit vector is } $$

If $$\theta$$ be the angle between the vectors $$a = 2\widehat i + 2\widehat j - \widehat k$$ and $$b = 6\widehat i - 3\widehat j + 2\widehat k$$, then

If x, y and z are non-zero real numbers and $$a = x\widehat i + 2\widehat j,b = y\widehat j + 3\widehat k$$ and $$c = x\widehat i + y\widehat j + z\widehat k$$ are such that $$a \times b = z\widehat i - 3\widehat j + \widehat k$$, then [a b c] is equal to

If $$\mathbf{p}=\hat{i}+\hat{j}, \mathbf{q}=4 \hat{k}-\hat{j}$$ and $$\mathbf{r}=\hat{i}+\hat{k}$$, then the unit vector in the direction of $$3 p+q-2 r$$ is

The vector that must be added to $$\widehat i - 3\widehat j + 2\widehat k$$ and $$3\widehat i + 6\widehat j - 7\widehat k$$ so resultant vector is a unit vector along the X-axis is

If |a| = 8, |b| = 3 and |a $$\times$$ b| = 12, then find the angle between a and b.

If for $$a = 2\widehat i + 3\widehat j + \widehat k,b = \widehat i - 2\widehat j + \widehat k$$ and $$c = - 3\widehat i + \widehat j + 2\widehat k$$, then find $$[a\,b\,c]$$.

If a and b are vectors such that $$|a + b|=|a-b|$$, then the angle between a and b is

If $$a = 2\widehat i + 3\widehat j - \widehat k,b = \widehat i + 2\widehat j - 5\widehat k,c = 3\widehat i + 5\widehat j - \widehat k$$, then a vector perpendicular to a and in the plane containing b and c is

OA and BO are two vectors of magnitudes 5 and 6 respectively. If $$\angle BOA=60^\circ$$, then OA . OB is equal to