You visited us 1 times! Enjoying our articles? Unlock Full Access!

Multiplication with Vectors

If A= 2i+2j...

Question

If $A = 2 i + 2 j + 3 k, B = - i + 2 j + k$ and $C = 3 i + j,$ and A+ tB is perpendicular to C then determine t.

- 8

No worries! We‘ve got your back. Try BYJU‘S free classes today!

- 4

No worries! We‘ve got your back. Try BYJU‘S free classes today!

4

No worries! We‘ve got your back. Try BYJU‘S free classes today!

8

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D $8$
$A = 2^i + 2^j + 3^k; B =^i + 2^j +^k; C = 3^i +^j$
$∴ A + t B = (2 - t)^i + (2 + 2 t)^j + (3 + t)^k$ ...(1)
$C = 3^i +^j$ ...(2)
Since (1) and (2) are perpendicular, their dot product is zero.
$∴ 6 - 3 t + 2 + 2 t = 0$ or
$8 - t = 0$ or
$t = 8$

Suggest Corrections

Similar questions

a = 2 i + 2 j + 3 k, b = - 1 + 2 j + k

c = 3 i + j

a + t b

c

t

A = 2 i + 2 j + 4 k, B = - i + 2 j + k

C = 3 i + j,

A + t B

C

t

\vec{a} = 2 \hat{i} + 2 \hat{j} + 3 \hat{k}, \vec{b} = - \hat{i} + 2 \hat{j} + \hat{k} and \vec{c} = 3 \hat{i} + \hat{j}

\vec{a} + λ \vec{b}

\vec{c}

[\vec{a} \vec{b} \vec{c}]

\vec{a} = 2 \hat{i} - 3 \hat{j}, \vec{b} = \hat{i} + \hat{j} - \hat{k} and \vec{c} = 3 \hat{i} - \hat{k}

\vec{a} = \hat{i} - 2 \hat{j} + 3 \hat{k}, \vec{b} = 2 \hat{i} + \hat{j} - \hat{k} and \vec{c} = \hat{j} + \hat{k}

\vec{a} = 2 \hat{i} + 3 \hat{j} + \hat{k}, \vec{b} = \hat{i} - 2 \hat{j} + \hat{k} and \vec{c} = - 3 \hat{i} + \hat{j} + 2 \hat{k}

[\vec{a} \vec{b} \vec{c}]

\vec{a} = 2 \hat{i} - 3 \hat{j}, \vec{b} = \hat{i} + \hat{j} - \hat{k} and \vec{c} = 3 \hat{i} - \hat{k}

\vec{a} = \hat{i} - 2 \hat{j} + 3 \hat{k}, \vec{b} = 2 \hat{i} + \hat{j} - \hat{k} and \vec{c} = \hat{j} + \hat{k}

Join BYJU'S Learning Program