Basics of Vectors

IMPORTANT

Basics of Vectors: Overview

This topic covers concepts such as Vector, Vector and Scalar Quantities, Representations of a Vector, Magnitude and Direction of a Vector, Direction Cosines and Direction Ratios of a Vector, Types of Vectors, Zero Vector, etc.

Important Questions on Basics of Vectors

MEDIUM
IMPORTANT

If   a , b , c  be vectors such that a + b + c =0,| a |=3,| b |=4and| c |=5 . The value of   a . b + b . c + c . a would be:

EASY
IMPORTANT

What would be the value of   λ  which makes the vectors  a,b,c  coplanar where  a=4i^6j^2k^,b=i^+4j^+3k^ and c=8i^j^+λk^

EASY
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If a vector A is multiplied by a scalar 0 then resultant is

EASY
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If a unit vector is represented by   0.5 i ^ +0.8 j ^ +c k ^ ,  the value of c is:

EASY
IMPORTANT

Vectors a and b are non-collinear. For what value of α are the vectors u=α-2a+b and v=2+3αa-3b collinear?

EASY
IMPORTANT

Find the magnitude of the following free vector X=-6i^-3j^-2k^.

EASY
IMPORTANT

Find the magnitude of the following free vector X=-2i^+3j^+6k^.

EASY
IMPORTANT

Find the magnitude of the following free vector a=2i^+j^+2k^

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Check whether the following vectors are anti-parallel or not.

a=-4i^-8j^ and b=i^+2j^.

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Check whether the following vectors are anti-parallel or not.

a=i^+j^ and b=-4i^-4j^.

EASY
IMPORTANT

If a=2i^+3j^+4k^. Find magnitude of 5a.

EASY
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If a=2i^+3j^+4k^. Find magnitude of 4a.

EASY
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If a=2i^+3j^+4k^. Find magnitude of 2a.

EASY
IMPORTANT

A vector in Cartesian form is given as p=2,3,4. Find vector 2p in Cartesian form.

EASY
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A vector in Cartesian form is given as p=2,3,4. Find vector -p in Cartesian form.

EASY
IMPORTANT

A vector in Cartesian form is given as p=1,2,3. Find vector -p in Cartesian form.

EASY
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A vector in Cartesian form is given as p=1,2,3. Find vector 4p in Cartesian form.

EASY
IMPORTANT

If a=2i^+3j^+4k^. Find magnitude of 3a.

EASY
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A vector in Cartesian form is given as p=1,2,3. Find vector 2p in Cartesian form.

EASY
IMPORTANT

a=4i^+2j^+3k^, find 3a.